Determination of Total Vector Error of the Phasor Measurement Unit (PMU) Using the Phase Angle Error of a Constant Amplitude Voltage Signal

This paper investigates the effect of the Phase Angle Error of a Constant Amplitude Voltage signal in determining the Total Vector Error (TVE) of the Phasor Measurement Unit (PMU) using MATLAB/Simulink. The phase angle error is measured as a function of time in microseconds at four points on the IEEE 14-bus system. When the 1 pps Global Positioning System (GPS) signal to the PMU is lost, sampling of voltage signals on the power grid is done at different rates as it is a function of time. The relationship between the PMU measured signal phase angle and the sampling rate is established by injecting a constant amplitude signal at two different points on the grid. In the simulation, 64 cycles per second is used as the reference while 24 cycles per second is used to represent the fault condition. Results show that a change in the sampling rate from 64 bps to 24 bps in the PMUs resulted in phase angle error in the voltage signals measured by the PMU at four VI Measurement points. The phase angle error measurement that was determined as a time function was used to determine the TVE. Results show that (TVE) was more than 1% in all the cases.

Angle measurement error and compensation for pitched rotation of circular grating

As circular grating is not vertical to the shaft,the angle measurement error of the circular grating is analyzed.Based on the moire fringe equations in pitched condition,the mathematic model of the angle measurement error is derived.The paper comes to the conclusion that the nonorthogonal angle between the circular grating and the shaft leads to the second harmonic error of the angle measurement,and the correctness of the result is proved by the experimental data.The method of the error compensation is presented,and the angle measurement accuracy of the circular grating is improved by the error compensation.

Effects of laser beam divergence angle on airborne LIDAR positioning errors

The influence of laser beam divergence angle on the positioning accuracy of scanning airborne light detection and ranging （LIDAR） is analyzed and simulated. Based on the data process and positioning principle of airborne LIDAR, the errors from pulse broadening induced by laser beam di vergence angle are modeled and qualitatively analyzed for different terrain surfaces. Simulated results of positioning errors and suggestions to reduce them are given for the flat surface, the downhill of slope surface, and the uphill surface.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

Orthogonality of inductosyn angle-measuring system error and error-separating technology

Round inductosyn is widely used in inertial navigation test equipment, and its accuracy has significant effect on the general accuracy of the equipment. Four main errors of round inductosyn,i.e. the first-order long-period (360°) harmonic error, the second-order long-period harmonic error, the first-order short-period harmonic error and the second-order short-period harmonic error, are described, and the orthogonality of these four kinds of errors is studied. An error separating technology is proposed to separate these four kinds of errors, and in the process of separating the short-period harmonic errors, the arrangement in the order of decimal part of the angle pitch number can be omitted. The effectiveness of the technology proposed is proved through measuring and adjusting the angular errors.

THE ANGLE ERROR ESTIMATE METHOD IN THE WIDE SWATH SAR BASING ON MULTI-RECEIVER

The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error of view and target height. A method is proposed in this paper to estimate the angle error from the return signal. The method makes use of the relationship between the view angle error and the signal correlation of the subswaths to estimate the angle error. The precision of this method is analyzed by the law of great number and it turns out to be in direct proportion to the root square number of averaging. The simulation result is given and the angle precision is 0.025°.

A Steady-State Errors Correction Method for Eliminating Measurement Errors

This paper proposes a steady-state errors correction(SSEC)method for eliminating measurement errors.This method is based on the detections of error signal E(s)and output C(s)which generate an expected output R(s).In comparison with the conventional solutions which are based on detecting the expected output R(s)and output C(s)to obtain error signal E(s),the measurement errors are eliminated even the error might be at a significant level.Moreover,it is possible that the individual debugging by regulating the coefficient K for every member of the multiple objectives achieves the optimization of the open loop gain.Therefore,this simple method can be applied to the weak coupling and multiple objectives system,which is usually controlled by complex controller.The principle of eliminating measurement errors is derived analytically,and the advantages comparing with the conventional solutions are depicted.Based on the SSEC method analysis,an application of this method for an active power filter(APF)is investigated and the effectiveness and viability of the scheme are demonstrated through the simulation and experimental verifications.

Trajectory shaping guidance law with terminal impact angle constraint

In order to strike hard targets underground or warships and tanks with expected impact angle by missiles or guided bombs, trajectory shaping guidance law with terminal position and impact angle constraints is derived based on linear quadratic optimal control theory. The required accelera- tion expressed by impact angle and heading error is obtained in lag-free guidance system in order to find the optimal relationship of those angles in terminal phase. The adjoint systems of miss distance and impact angle error of first-order guidance system are established based on statistical linearization adjoint method （SLAM） in order to study the impact performances of the guidance law. Simulation results show that the miss distance and impact angle error of trajectory shaping guidance law are both according with the impact position and angle constraint and the required acceleration at impact can be decreased by an optimal relationship of impact angle and heading error.

Roll angle measurement system based on triaxial magneto-resistive sensor

Aiming at large error when inertial devices measure the roll angle under high overload conditions,the article designs one kind of roll angle measurement system based on magneto-resistive sensor which calculates the roll angle by micro controller STM32.Experiment results of a triaxial turntable show that using magneto-resistive sensor to measure roll angle is feasible and of high accuracy,and it can calculate the roll angle of the conventional projectile with the error in 1°.

Design of the Rotation Angle Measurement System for the Atmospheric Dispersion Corrector (ADC)

In order to measure the rotation angle error of the worm and gear mechanisms in the atmospheric dispersion corrector( ADC),a novel measurement system based on the autocollimator is designed in this paper.Based on the position relations between the shaft and spot converged by rays of autocollimator,the rotation angle can be calculated quickly and conveniently using a brief algorithm. An optical wedge is introduced to the measurement system for suppressing the awful measuring error caused by the axial wobbly error. The measurement system can measure the shaft rotation angle at any rotation position,which is the novel usage of the two-dimensional autocollimator. Its optical layout is very simple. Only an optical wedge and two plane mirrors are needed besides the autocollimator. The measurement accuracy of the proposed method is less than±0.5 arcmin. In the measurement of two worms and gears mechanisms in ADC,the rotation angle error are±0.05° and ±0.07° respectively,which all satisfies the design demand( ±0.1°). The proposed measurement system can be also suits for some engineering fields.

A target group tracking algorithm for wireless sensor networks using azimuthal angle of arrival information

In this paper, we explore the technology of tracking a group of targets with correlated motions in a wireless sensor network. Since a group of targets moves collectively and is restricted within a limited region, it is not worth consuming scarce resources of sensors in computing the trajectory of each single target. Hence, in this paper, the problem is modeled as tracking a geographical continuous region covered by all targets. A tracking algorithm is proposed to estimate the region covered by the target group in each sampling period. Based on the locations of sensors and the azimuthal angle of arrival （AOA） information, the estimated region covering all the group members is obtained. Algorithm analysis provides the fundamental limits to the accuracy of localizing a target group. Simulation results show that the proposed algorithm is superior to the existing hull algorithm due to the reduction in estimation error, which is between 10% and 40% of the hull algorithm, with a similar density of sensors. And when the density of sensors increases, the localization accuracy of the proposed algorithm improves dramatically.

Angle measurement technology based on magnetization vector for narrow space applications

With the wide application of laser in the field of skin plastic surgery, micro laser galvanometer scanner has made great progress in this field with its portability. However, the measurement method used to measure the deflection angle of laser galvanometer in the narrow space of scanner with high precision remains to be studied. In this paper, an angle measurement method based on magnetic field is proposed, and the effect of the shapes of permanent magnets(PMs) on the measurement is studied by theoretical and experimental study under the condition that the maximum available space for the PMs is a 10 mm side cube. An angle measuring experimental device is set up, and the contrast experiment is carried out with different PMs which are the same as simulation. The experimental results show that cylindrical PM is more suitable than other PMs, which is consistent with the simulation results, and the maximum nonlinearity error is 0.562%. This method has the advantages of small volume,non-contact measurement, small moment of inertia, good dynamic response and no external excitation for the PMs, so it has a broad application prospect in micro laser galvanometer scanner.

Study on Initial Alignment Under Large Misalignment Angle

Misalignment angle error model describing the SINS mathematical platform error is presented in this paper following the idea of small misalignment angle error model and large azimuth misalignment angle error model.It can be considered that the three misalignment angles are independent of the rotational sequence in the misalignment error model,but not suitable in the large misalignment error model.The error angle of Euler platform is used to represent the three misalignment angles from theoretical navigation coordinate system to computational navigation coordinate system.The Euler platform error angle is utilized to represent the mathematical platform error and its physical meaning is very clear.The SINS nonlinear error model is deduced by using the error angle of Euler platform and is simplified under the condition of large azimuth error and small error.The simplified results are more comprehensive and accurate than the large azimuth misalignment error model.The damping SINS algorithm and its error model are proposed to change the structure of the strapdown inertial navigation algorithm by using the external damping information.The accuracy of SINS error model of large Euler platform error angle is simulated,and has strong practicability in initial alignment and is conducive to reducing the amount of calculation.

A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error

In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems.

Missile guidance law design based on free-time convergent error dynamics

To solve the finite-time error-tracking problem in mis-sile guidance,this paper presents a unified design approach through error dynamics and free-time convergence theory.The proposed approach is initiated by establishing a desired model for free-time convergent error dynamics,characterized by its independence from initial conditions and guidance parameters,and adjustable convergence time.This foundation facilitates the derivation of specific guidance laws that integrate constraints such as leading angle,impact angle,and impact time.The theoretical framework of this study elucidates the nuances and synergies between the proposed guidance laws and existing methodologies.Empirical evaluations through simulation comparisons underscore the enhanced accuracy and adaptability of the proposed laws.

Optimizing circumferential assembly angle of rotor parts connected by curvic couplings based on acquired tooth surface error data

Due to the excellent self-centering and load-carrying capability,curvic couplings have been widely used in advanced aero-engine rotors.However,curvic tooth surface errors lead to poor assembly precision.Traditional physical-master-gauge-based indirect tooth surface error measurement and circumferential assembly angle optimization methods have the disadvantages of high cost and weak generality.The unknown tooth surface fitting mechanism is a big barrier to assembly precision prediction and improvement.Therefore,this work puts forward a data-driven assembly simulation and optimization approach for aero-engine rotors connected by curvic couplings.The origin of curvic tooth surface error is deeply investigated.Using 5-axis sweep scan method,a large amount of high-precision curvic tooth surface data are acquired efficiently.Based on geometric models of parts,the fitting mechanism of curvic couplings is uncovered for assembly precision simulation and prediction.A circumferential assembly angle optimization model is developed to decrease axial and radial assembly runouts.Experimental results show that the assembly precision can be predicted accurately and improved dramatically.By uncovering the essential principle of the assembly precision formation and proposing circumferential assembly angle optimization model,this work is meaningful for assembly quality,efficiency and economy improvement of multistage aero-engine rotors connected by curvic couplings.

Theory and practice of hull dynamic deformation law and heading angle transfer error correction

In order to meet the demand of high-precision heading angle transmission in the transfer alignment of inertial navigation system on moving base,the analytical function relationship between the hull deforma-tion and the turning angular velocity and angular acceleration was derived by using the classical beam theory based on the analysis of the equivalent load exerted by the hydrodynamic force and inertia force on the hull structure during the turning process under the combined action of the steering rudder mo-ment and wave force.The objective law between the angular motion and the azimuth deformation angle of the hull under the combined action of maneuvering and sea waves was revealed.Finally,the correc-tion coefficients were determined according to the left turn and right turn motions of the hull by using the measured data of the ship in the sea trial during the S-shape maneuvering navigation,and the az-imuth deformation angle correction was completed.The results indicated that the application of the Qu’s bending deformation correction formula could greatly reduce the influence of the hull flexural deforma-tion on the heading angle accuracy,meet the needs of high-precision heading angle transmission,and fully verify the correctness of the hull azimuth deformation law and the heading angle transmission er-ror correction theory.This theory and method provided technical support for establishing high-precision distributed digital reference in the field of transfer alignment of inertial navigation on moving base and the application of heading angle transfer of other shipborne equipment.

Dynamics and Attitude Error Analysis for Dock Test System of Small Satellite

To analyze the attitude errors of vertical docking test system of small satellite,the static error and kinematic error of test system are considered.The working principle of test system and coordinate of actuator are introduced.The model of friction torque on the joints and torque on docking mechanism are built.Dynamics equation of actuator is built by the Lagrange equation and the Nielsen equation.Under the condition of 24 different angle groups,the calculation of dynamics equation is built by using MATLAB/SIMULINK platform and the kinematic errors of actuator are obtained.The attitude error models of docking mechanism are built.Results shows that the main angle error sources of yaw,row,pitch are not identical.The attitude error of yaw angle can be decreased by compensating the angle error around xaxis.The attitude error of row angle mainly originates in the system error,and it can be eliminated by adjusting non-orthogonal degree.

Estimating the Baseline Error of Wide-Swath Altimeters Using Nadir Altimeters via Numerical Simulation

The baseline roll and length errors for wide-swath altimeters are major error sources in sea surface measurements that exhibit strong spatial characteristics in the cross-track direction.These errors can be identified and estimated in accordance with height differences at crossover points generated with nadir altimeters after excluding the interference from other error sources.Most of the wide-swath altimeter baseline estimation methods considered only the roll error in previous studies.A numerical simulation was conducted in this study using nadir altimeters to estimate the roll and length errors simultaneously to provide a selectable scheme for baseline error estimation and correction for future wide-swath altimeters.Results based on the parameters of the surface water and ocean topography mission and Sentinel-3A show that the correlation coefficient of the roll error between the estimated and simulated values is 0.89,while the correlation coefficient of the length error is 0.85.The sea surface height root mean square error(RMSE)can be reduced from 12.18 cm to 6.45 cm based on the two estimated results.The estimation effect can be increased by using multiple nadir altimeters to form an observation constellation.The numerical simulation of the five nadir altimeter constellation shows that the correlation coefficients of the roll and length errors would increase to 0.97,which reduces the sea surface height RMSE to 2.88 cm.In addition,the stability of this method is indicated in simulation experiments,which introduce different degrees of sea state errors.

Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.